At a café, 60 customers were asked about their drinks: 35 like tea and 28 like coffee. What is the greatest possible number of customers who like neither?

0Correct answerYour answer7Correct answerYour answer25Correct answerYour answer32Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

'Neither' is largest when the two groups overlap as much as possible.
The largest overlap puts all 28 coffee-lovers inside the 35 tea-lovers; then only 35 like at least one.
Neither $= 60 - 35 = 25$ .

Worth noting

0 is the SMALLEST possible 'neither'. 7 is just $35 - 28$ , a difference with no meaning here. 32 $(60 - 28)$ would need the 35 tea-lovers inside the 28 coffee-lovers, which is impossible.

Concept: Maximum of the 'neither' region
Typical timeTypical: 100 s
Your timeYours: —

The rule this testsCounting with overlapping sets

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Ten questions from Venn Diagrams, at your own pace.

At a café, 60 customers were asked about their drinks: 35 like tea and 28 like coffee. What is the greatest possible number of customers who like neither?

Explanation